optimal inclination facade

[fluida_mente]

hi, i have tried to deform a simple box, moving the south facing edge(between a wall and the ceiling) toward the vector of the sun on the hottest day ( average) in rome at midday, in order to decrease the incident light on the south face and decrease the inside temperature.

I started analyzing a not deformed box ( "volume 1" , red in the image) thermal analisys, seeing the solar exposure for the horizontal and vertical face, faced to south (overshadowing-ground reflections).the same I have done for the deformed box( "volume 2" ,green in the image) and for the other more deformed box("volume 3"blue).
The surface/volume ratio was constant for all the boxes (1.3), but obviously the deformed ones had larger faces exposed. the material for the external faces was brick plaster for the walls, and plaster insulation suspended for all the boxes.

what i soon noticed is that curiously the simple not deformed box had the less inside temperature during the afternoon (slightly higher in the morning), even though the solar exposure revealed the most average incident radiation than the other deformed boxes (less incident light but very high inside temperature during the afternoon ).

how is it possible? the s/v is the same, as i said before the surfaces in the deformed boxes are larger but with less incident light(the angle beetween the vector light of the sun at midday and the normal of the south face, or the ceiling, is higher in the deformed box, therefore further from the maximum 90° incidence. ) .if i'm not wrong setting up the problem, what is a good way to qualitatively control the shape, i mean, what is the factor to think about to optimize a shape for example in a hot climate, and in general what's the main factor that influence the inside temperature of a building.

thank you, i hope to be clear.
federico

[Mike Sealander]

One thing you might consider is that the more you deform your box, the greater the surface area of the envelope, and the larger the amount of ambient outdoor heat transferring into the envelope. I'm not sure if my theory is correctly explaining what Ecotect is doing, but think about envelope area optimization: the smallest area you can use to enclose a space is a spherical area.
In terms of how much sun is hitting your box, whether deformed or not, you have to consider the flattened area that is available for the sun to hit: looking at the box from the point of view of the sun, are you increasing or decreasing its apparent (2d) area? Angle of incidence criteria will only apply if your box is very shiny, and thus good at reflecting light hitting at a low angle of incidence. Even then, a shiny sphere may be better than a shiny deformed box with more apparent area.